Problem: $\dfrac{ 9b + 2c }{ 10 } = \dfrac{ -7b - 9d }{ 10 }$ Solve for $b$.
Answer: Notice that the left- and right- denominators are the same $\dfrac{ 9b + 2c }{ {10} } = \dfrac{ -7b - 9d }{ {10} }$ So we can multiply both sides by $10$ ${10} \cdot \dfrac{ 9b + 2c }{ {10} } = {10} \cdot \dfrac{ -7b - 9d }{ {10} }$ $9b + 2c = -7b - 9d $ Combine $b$ terms on the left. ${9b} + 2c = -{7b} - 9d$ ${16b} + 2c = -9d$ Move the $c$ term to the right. $16b + {2c} = -9d$ $16b = -9d - {2c}$ Isolate $b$ by dividing both sides by its coefficient. ${16}b = -9d - 2c$ $b = \dfrac{ -9d - 2c }{ {16} }$